276 citations · 4.5k across the 293 of their papers we have counts for
11 papers · 1 filter
Mixing for progressions in non-abelian groups
Terence Tao
We study the mixing properties of progressions , of length three and four in a model class of finite non-abelian groups, namely the special linear g…
Multiple recurrence in quasirandom groups
Vitaly Bergelson, Terence Tao
We establish a new mixing theorem for quasirandom groups (finite groups with no low-dimensional unitary representations) which, informally speaking, asserts that if are…
Expanding polynomials over finite fields of large characteristic, and a regularity lemma for definable sets
Terence Tao
Let $P: \F \times \F \to \F$ be a polynomial of bounded degree over a finite field $\F$ of large characteristic. In this paper we establish the following dichotomy: either is a…
On sets defining few ordinary lines
Ben Green, Terence Tao
Let P be a set of n points in the plane, not all on a line. We show that if n is large then there are at least n/2 ordinary lines, that is to say lines passing through exactly two…
Random matrices: Universality of local spectral statistics of non-Hermitian matrices
Terence Tao, Van Vu
It is a result of Ginibre that the normalized bulk -point correlation functions of a complex Gaussian matrix with independent entries of mean zero and unit variance…
New bounds for Szemeredi's theorem, Ia: Progressions of length 4 in finite field geometries revisited
Ben Green, Terence Tao
Let p > 4 be a prime. We show that the largest subset of F_p^n with no 4-term arithmetic progressions has cardinality << N(log N)^{-c}, where c = 2^{-22} and N := p^n. A result of…